Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -12}$ ${2x-3y = 2}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-5y = -10$ $\dfrac{-5y}{{-5}} = \dfrac{-10}{{-5}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x-2y = -12}\thinspace$ to find $x$ ${-2x - 2}{(2)}{= -12}$ $-2x-4 = -12$ $-2x-4{+4} = -12{+4}$ $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {2x-3y = 2}\thinspace$ and get the same answer for $x$ : ${2x - 3}{(2)}{= 2}$ ${x = 4}$